Question

A coin collector has $45 in just dimes and quarters in a piggy bank he counted all the coins and there are 240 total how many each type of each coin does he have

Answer 1

The number of dimes are 100 and number of quarters are 140.

Explanation:

Let the number of dimes be 'd' and quarters be 'q'.

Given:

The sum of amount is $45.

The total number of coins are 240.

1 dime = $0.10

∴ 'd' dimes =
`\$0.10d`

1 quarter = $0.25

∴ 'q' quarters =
`\$0.25q`

Now, as per question:

`d+m=240-----1\\0.1d+0.25q=45---2`

Multiplying equation (1) by -0.1 and adding the result to equation (2), we get:

`-0.1d-0.1q=240* -0.1\\-0.1d-0.1q=-24\\0.1d+0.25q=45\\-----------\\0.15q=21\\q=(21)/(0.15)=140\\\\d=240-q=240-140=100`

Therefore, the number of dimes are 100 and number of quarters are 140.